The first part of this thesis presents a novel design for DRAMs to provide self-refreshing cycles which vary with temperature dynamically to reduce power dissipation in a standby mode. The proposed design monitors the data loss of a memory cell which is resulted from the leakage current, and then adjusts the period of the self-refreshing cycles. The second part presents two fast half-swing CMOS circuits for NOR-NOR PLA implementation. An additional 1/2VDD voltage source and buffering transmission gates are inserted between the NOR planes of PLAs to erase the racing problem and shorten the rise delay as well as the fall delay of the output response such that the speed is enhanced.